docs: def isentropic_T_rise_compression(T1, P1, P2, k, eta=1):
      r'''Calculates the increase in temperature of a fluid which is compressed
      or expanded under isentropic, adiabatic conditions assuming constant
      Cp and Cv.  The polytropic model is the same equation; just provide `n`
      instead of `k` and use a polytropic efficienty for `eta` instead of a
      isentropic efficiency.
  
      .. math::
          T_2 = T_1 + \frac{\Delta T_s}{\eta_s} = T_1 \left\{1 + \frac{1}
          {\eta_s}\left[\left(\frac{P_2}{P_1}\right)^{(k-1)/k}-1\right]\right\}
  
      Parameters
      ----------
      T1 : float
          Initial temperature of gas [K]
      P1 : float
          Initial pressure of gas [Pa]
      P2 : float
          Final pressure of gas [Pa]
      k : float
          Isentropic exponent of the gas (Cp/Cv) or polytropic exponent `n` to
          use this as a polytropic model instead [-]
      eta : float
          Isentropic efficiency of the process or polytropic efficiency of the
          process to use this as a polytropic model instead [-]
  
      Returns
      -------
      T2 : float
          Final temperature of gas [K]
  
      Notes
      -----
      For the ideal case (`eta`=1), the model simplifies to:
  
      .. math::
          \frac{T_2}{T_1} = \left(\frac{P_2}{P_1}\right)^{(k-1)/k}
  
      Examples
      --------
      >>> isentropic_T_rise_compression(286.8, 54050, 432400, 1.4)
      519.5230938217768
  
      References
      ----------
      .. [1] Couper, James R., W. Roy Penney, and James R. Fair. Chemical Process
         Equipment: Selection and Design. 2nd ed. Amsterdam ; Boston: Gulf
         Professional Publishing, 2009.
      .. [2] GPSA. GPSA Engineering Data Book. 13th edition. Gas Processors
         Suppliers Association, Tulsa, OK, 2012.
      '''
      dT = T1*((P2/P1)**((k - 1.0)/k) - 1.0)/eta
      return T1 + dT